My example is that I'm I'm running the Pathfinder Beginner Box campaign with some people who have never played before. The party got through the first adventure (Black Fang's Dungeon). I was originally running it to level up independently of XP as the story progressed. However, one of the party has left the country and is getting replaced by another player who has played RPGs before.

I'm planning to bring this new player in with a new character in at level 2 due to balance issues (as discussed in chat).

What considerations do I need to take for this new character in terms of gold and loot?

1 Answer
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Your PF books and SRD have tables and advice on character wealth.

Pathfinder, like 3.x before it, has a clear wealth progression. About halfway down this page you'll find Table: Character Wealth by Level as well as some other useful tables and tips.

I'm not familiar with how closely the Beginner Box campaign follows the standard PF treasure-per-encounter suggestions (listed in a table just below the one mentioned above), but some combination of or choice between the standard wealth suggestions and the Beginner Box's treasure drops (look at how much wealth each of your existing party members have, and how much the guy who left had) should yield a good idea what to do for the new guy.

You'll probably want to tell your new player how much effective wealth he has available to him, and let him 'purchase' items before he starts play: maybe his PC bought them, maybe they're adventure treasure or inherited heirlooms, but starting with a lump sum and needing to find a town to buy stuff is probably going to slow the game down and strain credulity. Questions like this one might be helpful in determining any restrictions you'd like to put on his purchases.